SOLUTION: The side of one square is 5 units longer than that of another square. Their areas differ by 105 square units. The lengths of their sides are: (A) 5 and 10 units (B) 7.5 and 12.5

Question 281440: The side of one square is 5 units longer than that of another square. Their areas differ by 105 square units. The lengths of their sides are:
(A) 5 and 10 units (B) 7.5 and 12.5 units (C) 8 and 13 units
(D) 15 and 20 units (E) none of these

Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
The side of one square is 5 units longer than that of another square. Their areas differ by 105 square units. The lengths of their sides are:
(A) 5 and 10 units (B) 7.5 and 12.5 units (C) 8 and 13 units
(D) 15 and 20 units (E) none of these

Let x be the length of the sides of the smaller square. Then x+5 is the length of the sides of the larger square. Then the areas of the squares are x^2 and (x+5)^2 respectively.
So we have:
(x+5)^2 - x^2 = 105
Expanding using FOIL gives us:
x^2 + 10x + 25 - x^2 = 105
10x + 25 = 105
Solve for x and calculate x+5.
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